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Along-Track Moving Target Indication Algorithm in FMCW SAR

The geometry of an along-track moving target in a FMCW SAR system is illustrated in Fig. 5.10. In Fig. 5.10, the instantaneous slant range can be expressed as

Fig. 5.10 Geometry of an along-track moving target in FMCW SAR

Substitute Eq. 5.4.4 into Eq. 5.2.7, the echo of the along-track moving target can be presented as

The fourth term of Eq. 5.4.5 is the range walk induced by FMCW system, which is determined by the along-track velocity. The additional range walk is often removed as a phase error in the existing FMCW SAR GMTIm algorithms. However, it is actually a favorable factor for the moving target indication. After range compression and RCMC, the trajectories of the stationary targets are straight lines that are parallel to the azimuth direction, whereas the trajectories of the along-track moving targets are not parallel to the azimuth direction as a result of the residual range curvature and the additional range walk.

Hough transform was proposed by P.V.C. Hough (1962) for the image characteristic detection. It is widely used in digital image processing, especially in dealing with the straight line indication and parameter estimation. After the Hough transform, the RCM trajectories in the scene are transformed into peaks. In the Hough transform domain, the amplitudes and locations of the peaks indicate the linearity and the slopes of the RCM trajectories, respectively. Since the slopes of the trajectories of the stationary targets and the moving targets are different, the peaks are located at different locations. By differentiating the locations of the peaks, the stationary targets can be suppressed and the along-track moving targets can be

detected. The relationship between the angle в of Hough transform and the along-track velocity is

The flowchart of the proposed algorithm is shown in Fig. 5.11.

Simulated data is employed to evaluate the performance of the proposed algorithm. Three stationary targets (ST1, ST2, and ST3) and two moving target (MT1 and MT2) are set in the scene, and an alpha-stable distribution noise with stability parameter a equals 1.5 is added to the echo to simulate the clutter of the real FMCW SAR data. The system parameters of the typical FMCW SAR are listed in Table 5.1, and the information of the five targets is listed in Table 5.2.

Figure 5.12a shows the results of the Hough transform after the azimuth down-sampling and the range interpolation. The down-sampling rate and range interpolation rate are set as 4 and 32, respectively. The larger these two parameters are, the more distinctive the residual rang walk migration will be. However, the ratio of the interpolation rate to the down-sampling rate determines the data amount and calculation burden, thus the values should be chosen eclectically [20]. According to Fig. 5.12a, the peaks of the stationary targets are located at regions around в = 0° and в = 180°, and the peaks of the moving targets are located away from these regions. Figure 5.12b illustrates the result after setting the regions в = 0°-5° and в = 175°-180° to zeros. The spectra of the stationary targets have been suppressed, and the peaks of the moving targets are contained. The amplitude image of all the targets, which is the indication of the linearity of the trajectories, is shown in Fig. 5.12c. The amplitude peaks (tagged by the rectangles) of ST1, ST2, and ST3 are 9, 11, 7, respectively, and those of MT1 and MT2 are 24 and 21, respectively. It is noted that the amplitudes of the moving targets are larger than those of the stationary targets. The result of the CFAR detection is shown in Fig. 5.12d. We can see from Fig. 5.12d that the energy of the stationary targets is eliminated, and the moving targets MT1 and MT2 are detected.

With the result of the Hough transform, the along-track velocities of the moving targets can also be estimated, and in turn the targets can be focused and relocated in the stationary image. Note that before azimuth refocusing, the additional range walk of the moving target must be corrected. Figure 5.13 shows the comparison of azimuth imaging of MT1 before and after additional range walk correction. From

Flowchart of the proposed algorithm

Fig. 5.11 Flowchart of the proposed algorithm

Table 5.1 System parameters

Parameter

Value

Carrier frequency

1 x 1010 Hz

Pulse repetition frequency

500 Hz

Pulse bandwidth

1 x 108 Hz

Range sampling rate

2.67 x 105 Hz

Central slant range

1000 m

Reference range

600 m

Antenna size

1 m

Platform velocity

100 m s-1

Result of Hough transform, a before and b after the removal of the stationary targets. c The amplitude of peaks of the five targets after the clutter suppression. d CFAR detection results

Fig. 5.12 Result of Hough transform, a before and b after the removal of the stationary targets. c The amplitude of peaks of the five targets after the clutter suppression. d CFAR detection results

Table 5.2 Target parameters

Target

Slant range (m)

Along-track velocity (ms1)

MT1

1000

10

MT2

900

20

ST1

1200

0

ST2

1100

0

ST3

800

0

Notes MT1 and MT2 represent moving target 1 and 2, respectively. ST1, ST2, and ST3 represent stationary target 1, 2, and 3, respectively

Table 5.3 Imaging quality analysis

Target

Range direction

Azimuth direction

IRW

PSLR

ISLR

IRW

PSLR

ISLR

(samples)

(dB)

(dB)

(samples)

(dB)

(dB)

MT1

1.850

-25.320

-2.622

3.000

-14.706

-9.830

ST1

1.800

-25.312

-2.556

3.000

-14.827

-9.928

Notes MT1 represents moving target 1, and ST1 represents stationary target 1. IRW impulse response width, PSLR peak side lobe ratio, ISLR integrated side lobe ratio

Fig. 5.13 Azimuth compression result for the target MT1

, it can be observed that the azimuth resolution is improved after the correction of the additional range walk

Fig. 5.13, it can be observed that the azimuth resolution is improved after the correction of the additional range walk. Detailed imaging quality between MT1 and ST1 is compared in Table 5.3. From Table 5.3, the focusing performance of the moving target is convincing since it shares the same imaging quality with stationary targets.

 
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